1. Field of the Invention
This invention relates to cryptographic communications in general and, more particularly, to methods and systems for establishing authenticated and/or private communications between parties who initially share only a relatively insecure secret.
2. Description of the Related Art
Parties often wish to conduct private and authenticated communications. While privacy can be sought through physical means it is often more efficient and effective to employ cryptographic means. And while authentication can be sought through physically secure and dedicated facilities, it too can be accomplished more easily with cryptographic techniques.
Using classical cryptographic techniques, a party authenticates himself or herself to another party by revealing knowledge of a secret (e.g., a password) that is known only by the respective parties. When the secret is revealed, especially if it is communicated over a physically insecure communication channel, it is susceptible to eavesdropping. This permits the eavesdropper to learn the secret and to subsequently impersonate one of the parties.
The Kerberos authentication system of MIT's Project Athena attempts to solve this problem in the context of computer networks. R. M. Needham and M. D. Schroeder, "Using Encryption for Authentication in Large Networks of Computers," Communications of the ACM, Vol. 21, No. 12, 993-999 December 1978); and J. Steiner, C. Neumann, and J. I. Schiller, "An Authentication Service for Open Network System," Proc. Winter USENIX Conference, Dallas, 1988. According to the Kerberos system, each Kerberos system user is given a non-secret unique login ID and is allowed to choose a secret password. The password is conveyed by the user to the Kerberos system and is held in confidence by both parties. Because the password is kept a secret it may be used by the user to authenticate himself to the Kerberos system.
When a Kerberos system user desires access to a Kerberos computer, the user sends his or her login ID to the Kerberos computer with a request for access. While authentication could be accomplished by requiring that the user sends his or her password along with his or her ID, that technique has the serious disadvantage that an eavesdropper could readily ascertain the ID and corresponding password of the user.
To avoid this problem, the Kerberos system authenticates the identity of the user by creating a puzzle that can probably be solved only by the bona fide user. The puzzle can be thought of as a locked box, containing a message, that is secured with a combination lock. The puzzle is constructed by the Kerberos system so that the combination to the combination lock is the secret password known by the bona fide user associated with the received ID. The bona fide user, knowning his or her own password, can use the password to open the lock and recover the message inside. When the combination to the combination lock is randomly selected from a large number of possibilities it is infeasible for an impersonator to "pick" the lock.
The mechanism used to create the puzzle typically uses several steps. First, the Kerberos system generates a random number as the message to be conveyed to the user. Next, the Kerberos system makes a puzzle (containing the random number) such that the user's password is the key to solving the puzzle and recovering the message. For example, suppose that according to one class of puzzles each puzzle is equal to a random number plus a number representing the user's password. When the user's password is 3049 and the random number is 5294 the puzzle is 8343.
The puzzle is transmitted to the user by the Kerberos system. Continuing with the example, the user, knowing his or her own password, solves the puzzle and recovers the message by subtracting his or her password (3049) from the puzzle (8343) to recover the message (5294). An eavesdropper knowing the puzzle (8343) but not knowing the password is unlikely to discover the message. According to the Kerberos system all communications between the user and the Kerberos system after the first puzzle is sent are also in the form of puzzles. But the key to solving the subsequent puzzles is the random number contained in the first puzzle which the Kerberos system and a bona fide user would know. Authentication occurs implicitly when the user and the computer are able to communicate meaningfully. And because all of the communications are encrypted privacy is achieved.
A discussion on the nomenclature of cryptology is appropriate at this time. A class of puzzles is known as a "cryptographic system" or "cryptosystem." The process of making a puzzle is known as "encryption" and the process of solving a puzzle to recover the message inside is known as "decryption." The puzzle is called "ciphertext" and the message within the puzzle is called "plaintext." The members of a cryptosystem are distinguished by a cryptographic key or key. According to the scheme of a particular cryptosystem, a key is used to lock plaintext into ciphertext and is also used to unlock the ciphertext to recove the plaintext.
The key to making a specific puzzle (i.e., locking plaintext in ciphertext) is known as an "encryption key" and the key to solving a puzzle (i.e., recovering the plaintext from the ciphertext) is known as a "decryption key." When, according to the design of a particular cryptosystem, the encryption key and the decryption key are identical, the cryptosystem is known as a "symmetric cryptosystem." The cryptosystem illustrated above is a symmetric cryptosystem because the number 3049 is the key to both creating the puzzle and to solving it.
A cryptosystem that has an encryption key E and a different decryption key D such that it is computationally infeasible to determine D from E is known as an "asymmetric key cryptosystem" or a "public key cryptosystem." An asymmetric key cryptosystem is not a symmetric cryptosystem and is therefore useful for initiating secure communications between parties who typically have not previously communicated nor share a common secret key to a symmetric cryptosystem. In contradistinction to an asymmetric key cryptosystem, a public key distribution system permits two remote users to exchange messages back and forth until they arrive at a common key to a symmetric key cryptosystem. The fundamental requirement of an asymmetric key cryptosystem is that an eavesdropper knowing all /f the messages must find it computationally infeasible to compute the common key.
To avoid repetition of background material W. Diffie and M. E. Hellman, "New Directions in Cryptography," I.E.E.E. Transactions on Information Theory, Vol. IT-22, No. 6, pp. 644-654 (November 1976) and W. Diffie and M. E. Hellman, "Privacy and Authentication: An Introduction to Cryptography," Proceedings of the I.E.E.E., Vol. 67, No. 3, pp. 397-427 (March 1979) are hereby incorporated by reference.
Returning to the Kerberos system, an eavesdropper on a communications channel utilizing the Kerberos system sees only the person's login ID transmitted in the clear: something that is already public knowledge. The person's password is never explicitly transmitted and the key and subsequent messages are encrypted and hence ostensibly secure. The Kerberos system, however, has a number of limitations and some weaknesses. S. M. Bellovin and M. Meritt, "Limitations of the Kerberos Authentication System," Proc. Winter USENIX Conference, Dallas, (1991). People pick bad passwords, and either forget, write down, or resent good ones. This allows an eavesdropper to passively record encrypted messages, and to run a modified brute force attack on a password by decrypting encrypted messages with candidate passwords until intelligible plaintext is created. Kerberos has additional flaws, but illustrates a weakness common to all classical two-party key exchange protocols: the cryptographic passwords are susceptible to off-line, brute-force attacks. Nevertheless, such key exchange protocols may be appropriate when the passwords are long randomly selected strings, but pose considerable difficulty when the passwords are chosen by naive users.
Other attempts at avoiding the problem of off-line password guessing attacks include that described by T. M. A. Lomas, L. Gong, J. H. Saltzer, and R. M. Needham in "Reducing Risks from Poorly Chosen Keys," Proceedings of the Twelfth ACM Symposium on Operating System Principles, SIGOPS, 14-18 (December 1989); and L. Gong, "Verifiable-text Attacks in Cryptographic Protocols," Proc. of the I.E.E.E. INFOCOM--The Conf. on Computer Communications, (1990). Lomas et al. teach a protocol that frustrates most cryptanalytic attacks but requires, for purposes of authentication, that each party know, in addition to their respective passwords a password, a public key to an asymmetric key cryptosystem. If the public key is to provide any reasonable level of security it cannot be easily memorized.